Post navigation

2 thoughts on “What Do We Mean by “Assume”?”

It has been interesting to me to see older math books begin sentences with “We assume that…”

I should open up my modern algebra texts and see what sort of terminology is used. I recently found an article in an older newsletter of the AMA written as an OP/Ed piece saying that we need to spend more time discussing with students what axioms are and why they are needed. Even in courses in which some subject matter is developed axiomatically (I guess Euclidean geometry is all that’s left) they claim is that the role of the axioms themselves is ignored.

This morning I was flipping through one of the older Dolicanis and they stated two axioms (to be assumed) and yet the second axiom was easily derivable from the first one.

Even in elementary school, I encourage my students to notice what assumptions are inherent in their word problems. I have heard teachers tell students to always ignore the word “if” in word problems, but to me, that is one of the most important words. It is laying out the foundation, the assumption, that the rest of the problem is based on.

I copied off the beginnings of Euclid for my geometry students, and they gave me the “You’re out of your mind!” look. A point is what?! I have managed to draw a little bit of axiomatic reasoning from them, with plenty of coaching, but most of the time they leap to assuming the conclusion and using it to justify their intermediate steps.

Browse the Blog Posts by Category

Fantasy Adventures by a Homeschooled Teen Novelist

Privacy Notice

If you want to comment on a post, we ask for your name (you can use a pseudonym) and email address‌—‌your home website is optional, for those who want the link. This helps us detect and avoid spam comments.

If you subscribe to blog posts by email (the blue envelope icon in the social media links above), those come from Feedburner, which is a Google service. You can read Google’s privacy policy here.

If you ask to receive updates about our books, we use your email address only to send you the newsletter(s) you request. These updates will include promotional material such as notice of a book release, limited-time discount prices, or other news.

We will not contact you directly unless it’s necessary to reply to your comment or question. For instance, if you offered to host the Playful Math Education Blog Carnival, we’ll need to confirm your date and send you information. We LOVE carnival hosts!

We do not share your name or email, except where it’s necessary to provide the service (comment posting or newletter) you requested, or unless the law requires us to do so.

Affiliate Disclosure

Almost all of the book covers featured on this site link to Amazon.com‌—‌either directly or through a service called Skimlinks‌—‌where you can read descriptions and reviews, and where I earn a small commission if you actually buy a book. But if you have access to a good library loan system, you should be able to read most of the books for free.Amazon.com Privacy PolicySkimlinks Privacy Policy